【摘要】 考虑对流扩散方程:Nbui(u)t=div(ρα|▽u| p-2▽u)+∑Ni=bi(u)/xi,(x,t)∈QT=Ω×(0,T)其中对流项∑Ni=bi(u)/xi满足bi(s)≤c|s|1+β,b′i(s)≤c|s|β.利用抛物正则化方法讨论该对流方程初边值问题解的定义,并在(p-2)/2>α>1下证明该问题存在唯一的弱解.更多还原

【Abstract】 The diffusion convection equation with boundary degeneracy Nbui(u)t=div(ρα|▽u| p-2▽u)+∑Ni=bi(u)/xi,(x,t)∈QT=Ω×(0,T)was researched by the parabolic regularization method,where the convective term ∑Ni=bi(u)/xi satisfies bi(s)≤c|s|1+β,b′i(s)≤c|s|β.We also studied how to quote the initial boundary value problem,and proved the existence and the uniqueness of the solutions under some additional conditions such as(p-2)/2>α>1.更多还原